Numerical validation of kinetic theory for interacting soliton gases

Paper Title:

Riemann problem for polychromatic soliton gases: a testbed for the spectral kinetic theory

Published on:

8 May 2024

Primary Category:

Pattern Formation and Solitons

Paper Authors:

T. Congy,

H. T. Carr,

G. Roberti,

G. A. El

Bullets

Key Details

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Develops analytical solutions for Riemann problem of interacting polychromatic soliton gases

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Presents novel numerical method combining soliton condensate theory and generalized hydrodynamics

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Implements efficient algorithm to synthesize dense, uniform n-soliton ensembles

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Performs systematic comparison between kinetic theory and numerical simulations

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Provides robust validation of spectral kinetic theory for dense soliton gas interactions

Explore the topics in this paper

collision models

kdv equation

kinetic theory

nls equation

soliton interactions

AI generated summary

Numerical validation of kinetic theory for interacting soliton gases

This paper uses the Riemann problem for interacting soliton gases to validate the spectral kinetic theory for the KdV and focusing NLS equations. It develops analytical solutions and numerical methods to model collisions between dense, polychromatic soliton gases composed of distinct monochromatic components. Comparisons are made between theoretical predictions and numerical simulations, providing robust confirmation of the kinetic theory in a broad parameter range.